NO REVERSE

Hi, my name is Vitaliy, and I own a Honda Civic 2003 EX. I have a problem with my reverse. Well more like I dont have reverse at all, for a about a year now due to the fact that I got a price quote on transmission replacement or fix and it was just little more the the price of the whole car. But now that I have been driving for almost a year without reverse make me wonder if it could be something else other than transmission.
English is my 2nd language. Sorry for bad spellcheck.
more detail.
when I drive car works perfectly without any weird sound or other problems. But if I switch to reverse the cars make the grinding or just unpleasant noise and it doesnt reverse.
CODES that I got were P0420, P0131. I did order O2 sensor that im going to replace this weekends. Other than that. I DO NOT have an engine light on. And yes the light work when I start the car. Cant really think of anything else useful to tell you. But I guess my question is. Could something else other then transmission cause my reverse problem and how likely>?